(1) It's important to understand social/demographic changes that are taking place and to better understand the direction in which the country is heading and perhaps how to prepare for that. For example, if we see that women are delaying childbearing more and more, then we know that that might have an impact on the number of schools we should build, or at least the timing of building those schools. Let's say we survey 169 randomly selected mothers and we nd that the age at which they gave birth to their rst child is normally distributed, with a mean of 26.0 years and a standard deviation of 3.25 years. (8 points total) (a) What is the standard error of the mean (to 2 decimal places)? (2 points) (b) What is the probability that the true mean age at rst birth for women (i.e., for the entire population from which this sample was drawn) falls between 26.16 and 26.46 years of age (to 4 decimal places)? (6 points) (2) In the previous assignment, we examined a random sample of 300 adults and who were asked to assess their health, from \"Poor\" to \"Excellent.\" The proportion of pe0ple who were in \"Poor\" health was .100 and the standard error of that proportion was .0173. (9 points total) (a) What is the probability (to 4 decimal places) that the true population proportion of people in poor health is above .13? (3 points) (b) Between .11 and .12 (to 4 decimal places)? (6 points)